Solving an intersection of inequalities. Here we have two pretty simple inequalities that we’re looking for the intersection for. We don’t have anything to solve for, so for this I would just jump straight to a number line.

Draw a number line out. This right there is saying x is greater than 4. We have our 4, and here we’re dealing with open circle, because we’re not equal to, everything greater than that. X is less than -1, open circle, goes down.

We’re looking for the intersection; we’re looking for where these two things overlap. Here everything is less than -1; here everything is greater than 4. Is there really any overlap? Can we get one number that is both less -1 and greater than 4. Not really. Doesn’t make sense, and our number line shows that, that there’s really no place that these two things overlap.

There is no intersection; no number can satisfy both of these two statements, so therefore we have no intersection.